Most people think Delta’s award calendar is broken (and it is) but it can actually show Korean Air award space. Here’s how:

Use an origin city from the list above
Set destination to ICN
Choose dates, number of passengers, and cabin
Check “Book SkyMiles Award Ticket”
Check “My Dates are Flexible”
Check “Nonstop Flights Only”

Notice that the calendar is not aware of the blackout dates. However, the green days should be Korean Air award space. This trick works because Delta only has nonstops to Korea from Tokyo and Detroit. For any other origin city the calendar is picking up Korean Air flights.

You may need to specify flight times for the Delta agent to see all the flights. Find the flight schedules on Korean Air’s page. Choose the city pairs and dates, then click “weekly schedule” to get a display like this:

That should be enough to get you started.